I have not had an issue with a rejected password for 5 months. There are a number of issues I addressed to correct the problem. As some in this forum have suspected it is only the main account tied to the DSL modem from AT&T that has the password rejection. I have 4 sbcglobal/Yahoo mail accounts, 2 gmail, 1 live.com all accessed through the mail app on both the iPad and iMac and a Win7 mini using the Live Mail client. The only account to have the password problem is the main account associated with the AT&T modem.
The SBC accounts on my iMac are set up as POP accounts as well as the gmail and have been for more than 10 years. On iPad 3 they are set up as IMAP except for the main account. The main account is now set up on the iPad as a POP account. It was originally IMAP and at that time I had rejected password problems.
When the rejected password problem surfaced I disabled the main account on my iPad as I had just added it so I suspected it may be causing the problem and it does. I left it disabled for a few months and the problem did not return. I could always go to Yahoo/SBCglobal mail site and get my mail on the main account from the iPad but that is not efficient. Four weeks ago I deleted the main account from my iPad and reinstalled it on the iPad as a POP account. Since then No problems with rejected password.
In the iPad I do not have push or fetch turned on so the only time it gets mail is when I access the mail app. I do not want to be interrupted every time a message comes in. The same is true on the iMac the mail app only gets mail when I press the Get Mail button. I believe as was previously stated that the high frequency access of mail from the Yahoo IMAP server may add to the rejected password problem. I just updated to iOS 6 and everything seems to work properly.